NYC and new bike for transportation sounds like a bad idea to me.. it will get stolen..
There has been a few people that picked up a wally wart bike to ride to work in NYC.. $100 bike plus $100 lock. Obviously this would not be near as fun to ride, but won't get stolen so it is a plus. For decently priced track bikes.. check out specialized.. bianchie.. fuji they all make track bikes in the $500-600 range.. Other choice is to browse your local thrift shops pick up a older frame for $20-40.. and either redish the rear wheel, but preferable buy a fixed gear wheel.. rip off the extra rings in front and you'll be set for very little money great way to test the waters to see if you like it or not..